Finite Group Databasebeta

← D3×#3141 #11664472

Subgroups — D3×#3141 #11664472

Order 768.

2398 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#532C211yesmaximal, characteristic
2C2×D3×C4⋊Q8C211yesmaximal, characteristic, complemented
3C3×#3141C211yesmaximal, characteristic, complemented
4#83283C211yesmaximal, characteristic, complemented
5#83199C211yesmaximal, characteristic, complemented
6#81683C214yesmaximal, complemented
7D3×#489C214yesmaximal, complemented
8#81601C212yesmaximal, complemented
9D3×#487C212yesmaximal, complemented
10#81565C212yesmaximal, complemented
11D3×#486C212yesmaximal, complemented
12D3×#417C214yesmaximal, complemented
13#78878C214yesmaximal, complemented
14#78528C211yesmaximal, characteristic, complemented
15C4×D3×M16C211yesmaximal, characteristic, complemented
16C2×#3141—31nomaximal, Sylow
17C2×D3×#41C2212yes—
18C22×D3×Q8—21no—
19C3×#532C2211yescharacteristic
20C2×C3×C4⋊Q8C2211yescharacteristic, complemented
21#5832C2212yes—
22C2×#944—21no—
23C2×D3×M16C2212yes—
24#5725C2211yescharacteristic
25D3×C4⋊Q8—21no—
26D3×C4⋊Q8—21no—
27D3×C4⋊Q8—21no—
28D3×C4⋊Q8—21no—
29D3×C4⋊Q8C2211yescharacteristic
30D3×C4⋊Q8C2212yes—
31D3×C4⋊Q8C2212yes—
32D3×C4⋊Q8C2212yescomplemented
33D3×C4⋊Q8C2212yescomplemented
34#5716C2211yescharacteristic
35D3×#127C2211yescharacteristic
36D3×#124C2212yes—
37#5668C2212yes—
38D3×#121—21no—
39D3×#121—21no—
40#5596—21no—
41#5596—21no—
42#5548—21no—
43#5548—21no—
44C4×D3×D4—21no—
45C4×D3×D4—21no—
46C2×D3×C4⋊C4—21no—
47C2×D3×C4⋊C4C2212yes—
48C2×#888—21no—
49C2×#888C2212yescomplemented
50#5477C2211yescharacteristic
51C2×C42×D3C2211yescharacteristic
52C2×#869C2211yescharacteristic, complemented
53C3×#489C2214yescomplemented
54C3×#487C2212yescomplemented
55C3×#486C2212yescomplemented
56C3×#417C2214yescomplemented
57C3×C4×M16C2211yescharacteristic, complemented
58#5232C2214yescomplemented
59#5133C2214yescomplemented
60Dic3×M16C2212yescomplemented
61#5093C2212yescomplemented
62#5089C2214yescomplemented
63#5088C2212yescomplemented
64#5079C2212yescomplemented
65#5070C2212yescomplemented
66#5055C2214yescomplemented
67#4966C2214yescomplemented
68C4×#208C2211yescharacteristic, complemented
69#4803C2218yescomplemented
70D3×#103C2218yes—
71#4794C2218yescomplemented
72#4792C2218yescomplemented
73#4771C2218yescomplemented
74D3×#102C2218yes—
75#4765C2218yescomplemented
76#4760C2218yescomplemented
77#4714C2214yescomplemented
78#4707C2212yescomplemented
79D3×#97C2212yes—
80#4694C2212yescomplemented
81C4×ΓL(1,𝔽25)C2212yescomplemented
82C4×D3×C8C2212yes—
83#4681C2212yescomplemented
84C2×#532—31no—
85C22×C4⋊Q8—31no—
86#3141—34no—
87#3141—32no—
88#3141—32no—
89#3141—34no—
90#3141—31no—
91#3141—31no—
92#3141—31no—
93#3141D311yescharacteristic, direct product factor
94C2×#489—34no—
95C2×#487—32no—
96C2×#486—32no—
97C2×#417—34no—
98C2×C4×M16—31no—
99C2×C3×#41C2312yes—
100C22×C3×Q8—21no—
101D3×#41—216no—
102C2×#239C2312yes—
103C2×D3×Q8—22no—
104C2×D3×Q8—22no—
105C2×D3×Q8—22no—
106C2×D3×Q8—22no—
107C2×D3×Q8—48no—
108C2×D3×Q8C2312yes—
109C2×#237—22no—
110C2×#237C2312yes—
111C2×D3×D4—22no—
112C2×D3×D4—21no—
113C2×D3×D4—21no—
114C2×D3×D4C2312yes—
115C2×#235—22no—
116C2×#235C2312yes—
117C22×C4×D3—22no—
118C22×C4×D3—22no—
119C22×C4×D3D411yescharacteristic
120C22×C4×D3D411yescharacteristic
121C22×C4×D3C2311yescharacteristic
122C22×Dic6—21no—
123C22×Dic6—22no—
124C2×C3×M16C2312yes—
125C3×C4⋊Q8—21no—
126C3×C4⋊Q8—21no—
127C3×C4⋊Q8C2311yescharacteristic
128C3×C4⋊Q8C2312yes—
129C3×C4⋊Q8C2312yes—
130C3×#127C2311yescharacteristic
131C3×#124C2312yes—
132C3×#121—21no—
133C3×#121—21no—
134C3×C4×D4—21no—
135C3×C4×D4—21no—
136C2×C3×C4⋊C4—21no—
137C2×C3×C4⋊C4C2312yes—
138C2×C3×C42C2311yescharacteristic
139#947C2312yes—
140#944—22no—
141#944—22no—
142#944—22no—
143#944—22no—
144#944C2312yes—
145#940—21no—
146#940—21no—
147#940C2312yes—
148#939—22no—
149#939—22no—
150#938—21no—
151#938—21no—
152#936C2312yes—
153D4×Dic3—21no—
154D4×Dic3—21no—
155#930—21no—
156#930—21no—
157C4×#67—22no—
158C4×#67—22no—
159C2×C4⋊Dic3—21no—
160C2×C4⋊Dic3C2312yes—
161C2×Dic3⋊C4—22no—
162C2×Dic3⋊C4—22no—
163C2×C4×Dic3D411yescharacteristic
164C2×C4×Dic3D411yescharacteristic
165C2×C4×Dic3C2311yescharacteristic
166C2×#208C2312yes—
167D3×M16—28no—
168C2×ΓL(1,𝔽25)C2314yes—
169C2×D3×C8C2314yes—
170#895—21no—
171#895—21no—
172#893—21no—
173#893—21no—
174D3×C4⋊C4—22no—
175D3×C4⋊C4—22no—
176D3×C4⋊C4—22no—
177D3×C4⋊C4—22no—
178D3×C4⋊C4—22no—
179D3×C4⋊C4—22no—
180D3×C4⋊C4—21no—
181D3×C4⋊C4—21no—
182D3×C4⋊C4C2314yes—
183D3×C4⋊C4C2314yes—
184#888—22no—
185#888—22no—
186#888—22no—
187#888—22no—
188#888—22no—
189#888—22no—
190#888—21no—
191#888—21no—
192#888C2314yes—
193#888C2314yes—
194#885—22no—
195#885—22no—
196#884—22no—
197#884—22no—
198#67⋊C4—22no—
199#67⋊C4—22no—
200D3×C22⋊C4—22no—
201D3×C22⋊C4—22no—
202#875C2312yes—
203#874C2311yescharacteristic
204C4×D12—21no—
205C4×D12—21no—
206C42×D3D411yescharacteristic
207C42×D3D411yescharacteristic
208C42×D3D411yescharacteristic
209C42×D3D411yescharacteristic
210C42×D3C2311yescharacteristic
211C42×D3C2311yescharacteristic
212C42×D3C2311yescharacteristic
213C42×D3C2311yescharacteristic
214#869—21no—
215#869—21no—
216#869C2311yescharacteristic
217#869C2312yes—
218#869C2312yes—
219C3×#103C2318yes—
220C3×#102C2318yes—
221C3×#97C2312yes—
222C3×C4×C8C2312yes—
223#835C2318yes—
224#832C2318yes—
225#821C2318yes—
226#816C2318yes—
227#815C2314yes—
228C8×Dic3C2314yes—
229#810C2318yes—
230#809C2318yes—
231#803C2312yes—
232C4×C3⋊C8C2312yes—
233C22×#41—32no—
234C23×Q8—61no—
235C22×M16—32no—
236#532—32no—
237#532—31no—
238#532—31no—
239#532—32no—
240#532—31no—
241#532—61no—
242#532—61no—
243#532—61no—
244#532—61no—
245#532C2×D311yescharacteristic
246C2×C4⋊Q8—32no—
247C2×C4⋊Q8—32no—
248C2×C4⋊Q8—32no—
249C2×C4⋊Q8—32no—
250C2×C4⋊Q8—32no—
251C2×C4⋊Q8—31no—
252C2×C4⋊Q8—31no—
253C2×C4⋊Q8—61no—
254C2×C4⋊Q8—61no—
255C2×C4⋊Q8—61no—
256C2×C4⋊Q8—61no—
257C2×C4⋊Q8—61no—
258C2×C4⋊Q8—61no—
259C2×C4⋊Q8C2×D311yescharacteristic, complemented
260C2×#127—31no—
261C2×#124—32no—
262C2×#121—61no—
263C2×#121—61no—
264C2×C4×D4—61no—
265C2×C4×D4—61no—
266C22×C4⋊C4—32no—
267C22×C4⋊C4—61no—
268C22×C42—31no—
269#489—34no—
270#489—34no—
271#489—38no—
272#489—38no—
273#489—34no—
274#489C2×D314yescomplemented
275#487—32no—
276#487—32no—
277#487—38no—
278#487—32no—
279#487C2×D312yescomplemented
280#486—32no—
281#486—32no—
282#486—38no—
283#486—32no—
284#486C2×D312yescomplemented
285#417—34no—
286#417—34no—
287#417—34no—
288#417—38no—
289#417—38no—
290#417C2×D314yescomplemented
291C2×#103—38no—
292C2×#102—38no—
293C4×M16—32no—
294C4×M16—31no—
295C4×M16—32no—
296C4×M16—32no—
297C4×M16C2×D311yescharacteristic, complemented
298C2×#97—32no—
299C2×C4×C8—32no—
300C23×D3—22no—
301C23×D3C2×D411yescharacteristic
302C3×#41—28no—
303C2×C3×Q8—22no—
304C2×C3×Q8—22no—
305C2×C3×Q8—44no—
306C2×C3×Q8C2412yes—
307C2×C3×D4—22no—
308C2×C3×D4—21no—
309C2×C3×D4—21no—
310C2×C3×D4C2412yes—
311C22×C3×C4—22no—
312C22×C3×C4—22no—
313C22×C3×C4C2×D411yescharacteristic
314C22×C3×C4C2×D411yescharacteristic
315C22×C3×C4C2411yescharacteristic
316C2×#67—22no—
317C2×#67—22no—
318C2×#67—22no—
319C2×#67—22no—
320C2×#67—22no—
321C22×Dic3—22no—
322C22×Dic3—22no—
323C22×Dic3C2×D411yescharacteristic
324C22×Dic3C2×D411yescharacteristic
325C22×Dic3C2×D411yescharacteristic
326#239—28no—
327D3×Q8—28no—
328D3×Q8—48no—
329D3×Q8—48no—
330D3×Q8—48no—
331D3×Q8—48no—
332#237—28no—
333#237—48no—
334D3×D4—28no—
335D3×D4—48no—
336D3×D4—44no—
337D3×D4—44no—
338#235—28no—
339#235—48no—
340C2×D12—22no—
341C2×D12—21no—
342C2×D12—21no—
343C2×D12C2412yes—
344C2×C4×D3—24no—
345C2×C4×D3—24no—
346C2×C4×D3—22no—
347C2×C4×D3—24no—
348C2×C4×D3—24no—
349C2×C4×D3—22no—
350C2×C4×D3—22no—
351C2×C4×D3—48no—
352C2×C4×D3—48no—
353C2×C4×D3C2×D411yescharacteristic
354C2×C4×D3C2×D411yescharacteristic
355C2×C4×D3C2×D411yescharacteristic
356C2×C4×D3C2×D411yescharacteristic
357C2×C4×D3C2×D411yescharacteristic
358C2×C4×D3C2×D411yescharacteristic
359C2×C4×D3C2×D411yescharacteristic
360C2×C4×D3C2×D411yescharacteristic
361C2×C4×D3C2×D411yescharacteristic
362C2×C4×D3C2×D411yescharacteristic
363C2×C4×D3#4118yes—
364C2×C4×D3C2411yescharacteristic
365C2×C4×D3C2411yescharacteristic
366C2×Dic6—22no—
367C2×Dic6—22no—
368C2×Dic6—22no—
369C2×Dic6—24no—
370C2×Dic6—24no—
371C2×Dic6—48no—
372C2×Dic6—44no—
373C2×Dic6C2412yes—
374C3×M16—24no—
375C2×C3×C8C2414yes—
376C3×C4⋊C4—22no—
377C3×C4⋊C4—22no—
378C3×C4⋊C4—22no—
379C3×C4⋊C4—21no—
380C3×C4⋊C4—21no—
381C3×C4⋊C4C2414yes—
382C3×C22⋊C4—22no—
383C3×C22⋊C4—22no—
384C3×C42C2×D411yescharacteristic
385C3×C42C2×D411yescharacteristic
386C3×C42C2411yescharacteristic
387C3×C42C2411yescharacteristic
388#217—22no—
389#217—22no—
390(C2×D3)⋊C4—22no—
391(C2×D3)⋊C4—22no—
392(C2×D3)⋊C4—22no—
393(C2×D3)⋊C4—22no—
394C4⋊Dic3—22no—
395C4⋊Dic3—22no—
396C4⋊Dic3—22no—
397C4⋊Dic3—21no—
398C4⋊Dic3—21no—
399C4⋊Dic3C2414yes—
400Dic3⋊C4—22no—
401Dic3⋊C4—22no—
402Dic3⋊C4—24no—
403Dic3⋊C4—24no—
404Dic3⋊C4—24no—
405Dic3⋊C4—24no—
406C4×Dic3C2×D411yescharacteristic
407C4×Dic3C2×D411yescharacteristic
408C4×Dic3C2×D411yescharacteristic
409C4×Dic3C2×D411yescharacteristic
410C4×Dic3C2×D411yescharacteristic
411C4×Dic3C2×D411yescharacteristic
412C4×Dic3C2×D411yescharacteristic
413C4×Dic3C2×D411yescharacteristic
414C4×Dic3C2×D411yescharacteristic
415C4×Dic3C2×D411yescharacteristic
416C4×Dic3C2411yescharacteristic
417C4×Dic3C2411yescharacteristic
418#208—24no—
419C2×C3⋊C8C2414yes—
420ΓL(1,𝔽25)—28no—
421D3×C8—28no—
422C2×#41—32no—
423C2×#41—32no—
424C2×#41—32no—
425C2×#41—62no—
426C2×#41—62no—
427C2×#41—616no—
428C2×#41C22×D312yes—
429C22×Q8—21no—
430C22×Q8—32no—
431C22×Q8—62no—
432C22×Q8—62no—
433C22×Q8—62no—
434C22×Q8—62no—
435C22×Q8—62no—
436C22×Q8—61no—
437C22×Q8—128no—
438C22×D4—32no—
439C22×D4—61no—
440C22×D4—61no—
441C22×D4—62no—
442C23×C4—31no—
443C23×C4—31no—
444C23×C4—31no—
445C23×C4—62no—
446C23×C4—62no—
447C2×M16—32no—
448C2×M16—34no—
449C2×M16—68no—
450C2×M16C22×D312yes—
451C22×C8—34no—
452C4⋊Q8—21no—
453C4⋊Q8—21no—
454C4⋊Q8—34no—
455C4⋊Q8—34no—
456C4⋊Q8—32no—
457C4⋊Q8—32no—
458C4⋊Q8—32no—
459C4⋊Q8—31no—
460C4⋊Q8—62no—
461C4⋊Q8—62no—
462C4⋊Q8—62no—
463C4⋊Q8—62no—
464C4⋊Q8—62no—
465C4⋊Q8—62no—
466C4⋊Q8—61no—
467C4⋊Q8—61no—
468C4⋊Q8—62no—
469C4⋊Q8—62no—
470C4⋊Q8—62no—
471C4⋊Q8—62no—
472C4⋊Q8—61no—
473C4⋊Q8—61no—
474C4⋊Q8C22×D311yescharacteristic
475C4⋊Q8C22×D312yes—
476C4⋊Q8C22×D312yes—
477#127—32no—
478#127—31no—
479#127—61no—
480#127—61no—
481#127C22×D311yescharacteristic
482#124—32no—
483#124—32no—
484#124—32no—
485#124—62no—
486#124—62no—
487#124C22×D312yes—
488#121—21no—
489#121—21no—
490#121—62no—
491#121—62no—
492#121—61no—
493#121—61no—
494#121—61no—
495#121—61no—
496#121—62no—
497#121—62no—
498#121—61no—
499#121—61no—
500C4×D4—21no—
501C4×D4—21no—
502C4×D4—62no—
503C4×D4—62no—
504C4×D4—61no—
505C4×D4—61no—
506C4×D4—62no—
507C4×D4—62no—
508C4×D4—61no—
509C4×D4—61no—
510C4×D4—61no—
511C4×D4—61no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—32no—
514C2×C4⋊C4—34no—
515C2×C4⋊C4—34no—
516C2×C4⋊C4—62no—
517C2×C4⋊C4—62no—
518C2×C4⋊C4—62no—
519C2×C4⋊C4—62no—
520C2×C4⋊C4—62no—
521C2×C4⋊C4—62no—
522C2×C4⋊C4—61no—
523C2×C4⋊C4—61no—
524C2×C4⋊C4—62no—
525C2×C4⋊C4—62no—
526C2×C4⋊C4—61no—
527C2×C4⋊C4C22×D312yes—
528C2×C22⋊C4—62no—
529C2×C22⋊C4—62no—
530C2×C42—31no—
531C2×C42—31no—
532C2×C42—31no—
533C2×C42—31no—
534C2×C42—31no—
535C2×C42—31no—
536C2×C42—31no—
537C2×C42—31no—
538C2×C42—31no—
539C2×C42—31no—
540C2×C42—31no—
541C2×C42C22×D311yescharacteristic
542#103—38no—
543#103—38no—
544#103—38no—
545#103C22×D318yes—
546#102—38no—
547#102—38no—
548#102—38no—
549#102C22×D318yes—
550#97—34no—
551#97—32no—
552#97C22×D312yes—
553C4×C8—34no—
554C4×C8—32no—
555C4×C8C22×D312yes—
556C23×C3—22no—
557C23×C3C22×D411yescharacteristic
558C22×D3—22no—
559C22×D3—22no—
560C22×D3—22no—
561C22×D3—44no—
562C22×D3—44no—
563C22×D3—44no—
564C22×D3#12414yes—
565C22×D3C22×D411yescharacteristic
566C22×D3C22×D411yescharacteristic
567C3×Q8—24no—
568C3×Q8—44no—
569C3×Q8—44no—
570C3×D4—24no—
571C3×D4—44no—
572C3×D4—42no—
573C3×D4—42no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—24no—
577C2×C3×C4—22no—
578C2×C3×C4—44no—
579C2×C3×C4—44no—
580C2×C3×C4C22×D411yescharacteristic
581C2×C3×C4C22×D411yescharacteristic
582C2×C3×C4C22×D411yescharacteristic
583C2×C3×C4C22×D411yescharacteristic
584C2×C3×C4C22×D411yescharacteristic
585C2×C3×C4C2×#4114yes—
586C2×C3×C4C2511yescharacteristic
587#67—44no—
588#67—44no—
589#67—44no—
590#67—44no—
591#67—44no—
592C2×Dic3—22no—
593C2×Dic3—22no—
594C2×Dic3—24no—
595C2×Dic3—22no—
596C2×Dic3—44no—
597C2×Dic3—44no—
598C2×Dic3#12414yes—
599C2×Dic3C22×D411yescharacteristic
600C2×Dic3C22×D411yescharacteristic
601C2×Dic3C22×D411yescharacteristic
602C2×Dic3C22×D411yescharacteristic
603C2×Dic3C22×D411yescharacteristic
604C2×Dic3C22×D411yescharacteristic
605D12—24no—
606D12—44no—
607D12—42no—
608D12—42no—
609C4×D3—22no—
610C4×D3—22no—
611C4×D3—22no—
612C4×D3—22no—
613C4×D3—22no—
614C4×D3—22no—
615C4×D3—48no—
616C4×D3—44no—
617C4×D3—48no—
618C4×D3—44no—
619C4×D3—44no—
620C4×D3#12414yes—
621C4×D3#12414yes—
622C4×D3AGL(1,ℤ/8)14yes—
623C4×D3#13714yes—
624C4×D3C2×#4114yes—
625C4×D3C2×#4114yes—
626Dic6—24no—
627Dic6—48no—
628Dic6—44no—
629Dic6—44no—
630Dic6—44no—
631Dic6—48no—
632C3×C8—24no—
633C3⋊C8—24no—
634C24—31no—
635C24—62no—
636#41—28no—
637#41—68no—
638#41—68no—
639#41—68no—
640#41—128no—
641#41—128no—
642C2×Q8—22no—
643C2×Q8—22no—
644C2×Q8—32no—
645C2×Q8—44no—
646C2×Q8—62no—
647C2×Q8—64no—
648C2×Q8—64no—
649C2×Q8—68no—
650C2×Q8—62no—
651C2×Q8—62no—
652C2×Q8—124no—
653C2×Q8—128no—
654C2×Q8—128no—
655C2×Q8—128no—
656C2×Q8—128no—
657C2×Q8—128no—
658C2×Q8C23×D312yes—
659C2×D4—22no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—32no—
663C2×D4—62no—
664C2×D4—68no—
665C2×D4—62no—
666C2×D4—62no—
667C2×D4—62no—
668C2×D4—62no—
669C2×D4—62no—
670C2×D4—61no—
671C2×D4—61no—
672C2×D4—124no—
673C2×D4—124no—
674C2×D4—128no—
675C2×D4C23×D312yes—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—31no—
679C22×C4—31no—
680C22×C4—31no—
681C22×C4—31no—
682C22×C4—31no—
683C22×C4—38no—
684C22×C4—31no—
685C22×C4—31no—
686C22×C4—31no—
687C22×C4—31no—
688C22×C4—31no—
689C22×C4—31no—
690C22×C4—31no—
691C22×C4—31no—
692C22×C4—31no—
693C22×C4—31no—
694C22×C4—64no—
695C22×C4—64no—
696C22×C4—62no—
697C22×C4—62no—
698C22×C4—64no—
699C22×C4—64no—
700C22×C4—62no—
701C22×C4—62no—
702C22×C4—62no—
703C22×C4—128no—
704C22×C4—128no—
705C22×C4D3×D411yescharacteristic
706C22×C4D3×D411yescharacteristic
707C22×C4C23×D311yescharacteristic
708M16—24no—
709M16—68no—
710M16—64no—
711C2×C8—34no—
712C2×C8—68no—
713C2×C8C23×D314yes—
714C4⋊C4—22no—
715C4⋊C4—22no—
716C4⋊C4—22no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—34no—
720C4⋊C4—64no—
721C4⋊C4—64no—
722C4⋊C4—64no—
723C4⋊C4—64no—
724C4⋊C4—62no—
725C4⋊C4—62no—
726C4⋊C4—62no—
727C4⋊C4—62no—
728C4⋊C4—62no—
729C4⋊C4—61no—
730C4⋊C4—61no—
731C4⋊C4C23×D314yes—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—62no—
735C22⋊C4—62no—
736C22⋊C4—62no—
737C22⋊C4—62no—
738C22⋊C4—62no—
739C22⋊C4—62no—
740C42—31no—
741C42—31no—
742C42—31no—
743C42—31no—
744C42—31no—
745C42—31no—
746C42—31no—
747C42—31no—
748C42—31no—
749C42—31no—
750C42—31no—
751C42—31no—
752C42D3×D411yescharacteristic
753C42D3×D411yescharacteristic
754C42C23×D311yescharacteristic
755C42C23×D311yescharacteristic
756C22×C3—21no—
757C22×C3—21no—
758C22×C3—42no—
759C22×C3—42no—
760C22×C3—42no—
761C22×C3C2×#12412yes—
762C22×C3C23×D411yescharacteristic
763C2×D3—21no—
764C2×D3—21no—
765C2×D3—28no—
766C2×D3—42no—
767C2×D3—42no—
768C2×D3—42no—
769C2×D3—88no—
770C2×D3C2×#12412yes—
771C2×D3C2×#12412yes—
772C2×D3C2×AGL(1,ℤ/8)12yes—
773C2×D3C2×#13712yes—
774C3×C4—21no—
775C3×C4—21no—
776C3×C4—42no—
777C3×C4—44no—
778C3×C4C2×#12412yes—
779C3×C4C2×AGL(1,ℤ/8)12yes—
780C3×C4C2×#13712yes—
781C3×C4C22×#4112yes—
782Dic3—21no—
783Dic3—21no—
784Dic3—42no—
785Dic3—44no—
786Dic3C2×#12412yes—
787Dic3C2×#12412yes—
788Dic3C2×AGL(1,ℤ/8)12yes—
789Dic3C2×#13712yes—
790C23—22no—
791C23—31no—
792C23—34no—
793C23—31no—
794C23—62no—
795C23—62no—
796C23—62no—
797C23—124no—
798C23—124no—
799C23—124no—
800C23C2×D3×D411yescharacteristic
801Q8—24no—
802Q8—44no—
803Q8—44no—
804Q8—64no—
805Q8—124no—
806Q8—124no—
807Q8—128no—
808Q8—128no—
809Q8—124no—
810D4—24no—
811D4—44no—
812D4—42no—
813D4—42no—
814D4—64no—
815D4—124no—
816D4—124no—
817D4—124no—
818D4—124no—
819D4—124no—
820D4—124no—
821D4—122no—
822D4—122no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—24no—
827C2×C4—34no—
828C2×C4—31no—
829C2×C4—31no—
830C2×C4—31no—
831C2×C4—31no—
832C2×C4—34no—
833C2×C4—34no—
834C2×C4—34no—
835C2×C4—34no—
836C2×C4—34no—
837C2×C4—34no—
838C2×C4—31no—
839C2×C4—31no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—62no—
843C2×C4—62no—
844C2×C4—62no—
845C2×C4—62no—
846C2×C4—62no—
847C2×C4—62no—
848C2×C4—62no—
849C2×C4—62no—
850C2×C4—62no—
851C2×C4—64no—
852C2×C4—124no—
853C2×C4—124no—
854C2×C4—124no—
855C2×C4—128no—
856C2×C4—128no—
857C2×C4—124no—
858C2×C4—124no—
859C2×C4C2×D3×D411yescharacteristic
860C2×C4C2×D3×D411yescharacteristic
861C2×C4C2×D3×D411yescharacteristic
862C2×C4C2×D3×D411yescharacteristic
863C2×C4C2×D3×D411yescharacteristic
864C2×C4D3×#4114yes—
865C2×C4C24×D311yescharacteristic
866C8—24no—
867C8—64no—
868C2×C3—22no—
869C2×C3—82no—
870C2×C3C22×#12411yescharacteristic
871C2×C3C22×AGL(1,ℤ/8)11yescharacteristic
872C2×C3C22×#13711yescharacteristic
873D3—22no—
874D3—82no—
875D3#314114yesdirect product factor
876C22—21no—
877C22—21no—
878C22—32no—
879C22—32no—
880C22—32no—
881C22—32no—
882C22—42no—
883C22—42no—
884C22—42no—
885C22—68no—
886C22—61no—
887C22—61no—
888C22—122no—
889C22—122no—
890C22—122no—
891C22—248no—
892C22D3×#12412yes—
893C22C22×D3×D411yescharacteristic
894C4—21no—
895C4—21no—
896C4—32no—
897C4—32no—
898C4—32no—
899C4—32no—
900C4—42no—
901C4—44no—
902C4—61no—
903C4—61no—
904C4—122no—
905C4—124no—
906C4D3×#12412yes—
907C4D3×AGL(1,ℤ/8)12yes—
908C4D3×#13712yes—
909C4C2×D3×#4112yes—
910C3C2×#314111yescharacteristic, complemented, Sylow
911C2—22no—
912C2—34no—
913C2—62no—
914C2—82no—
915C2—242no—
916C2C2×D3×#12411yescharacteristic
917C2C2×D3×AGL(1,ℤ/8)11yescharacteristic
918C2C2×D3×#13711yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3141C2
socleC22×C3C23×D4
prime radicalD3×#532C2
hypercenter#3141D3
hypocenterC3C2×#3141
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3141

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×D3×C4⋊Q8C2semidirect
3. C3×#3141C2semidirect
4. #83283C2semidirect
5. #83199C2semidirect
6. #81683C2semidirect
7. D3×#489C2semidirect
8. #81601C2semidirect
9. D3×#487C2semidirect
10. #81565C2semidirect
11. D3×#486C2semidirect
12. D3×#417C2semidirect
13. #78878C2semidirect
14. #78528C2semidirect
15. C4×D3×M16C2semidirect
20. C2×C3×C4⋊Q8C22semidirect
32. D3×C4⋊Q8C22semidirect
33. D3×C4⋊Q8C22semidirect
49. C2×#888C22semidirect
52. C2×#869C22semidirect
53. C3×#489C22semidirect
54. C3×#487C22semidirect
55. C3×#486C22semidirect
56. C3×#417C22semidirect
57. C3×C4×M16C22semidirect
58. #5232C22semidirect
59. #5133C22semidirect
60. Dic3×M16C22semidirect
61. #5093C22semidirect
62. #5089C22semidirect
63. #5088C22semidirect
64. #5079C22semidirect
65. #5070C22semidirect
66. #5055C22semidirect
67. #4966C22semidirect
68. C4×#208C22semidirect
69. #4803C22semidirect
71. #4794C22semidirect
72. #4792C22semidirect
73. #4771C22semidirect
75. #4765C22semidirect
76. #4760C22semidirect
77. #4714C22semidirect
78. #4707C22semidirect
80. #4694C22semidirect
81. C4×ΓL(1,𝔽25)C22semidirect
83. #4681C22semidirect
93. #3141D3direct (N × H)
259. C2×C4⋊Q8C2×D3semidirect
274. #489C2×D3semidirect
279. #487C2×D3semidirect
284. #486C2×D3semidirect
290. #417C2×D3semidirect
297. C4×M16C2×D3semidirect
875. D3#3141direct (N × H)
910. C3C2×#3141semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
D3×#5322
C2×D3×C4⋊Q82
C3×#31412
#832832
#831992
#816832
D3×#4892
#816012
D3×#4872
#815652
D3×#4862
D3×#4172
#788782
#785282
C4×D3×M162
C2×#31413